Generalized localization for spherical partial sums of multiple Fourier series

DOI10.1007/s00041-019-09697-7zbMath1431.42015arXiv1901.03028OpenAlexW2972278171WikidataQ127286365 ScholiaQ127286365MaRDI QIDQ5919713

Ravshan Ashurov

Publication date: 21 November 2019

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.03028

zbMATH Keywords

spherical partial sumsmultiple Fourier seriesgeneralized localizationconvergence almost-everywhere

Mathematics Subject Classification ID

Harmonic analysis in several variables (42B99) Fourier series and coefficients in several variables (42B05) Summability in several variables (42B08)

Related Items (3)

Localisation of spectral sums corresponding to the sub-Laplacian on the Heisenberg group ⋮ Generalized localization and summability almost everywhere of multiple Fourier series and integrals ⋮ Multiple Fourier series and lattice point problems

Cites Work

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• The generalized localization for multiple Fourier integrals
• Regularity and integrability of spherical means
• Generalized localization of Fourier series with respect to the eigenfunctions of the Laplace operator in the classes \(L_ p\)
• Radial weights and mixed norm inequalities for the disc multiplier
• Pointwise Fourier inversion and localisation in \(\mathbb{R}^n\)
• On the Pinsky phenomenon
• Almost Everywhere Summability of Fourier Integrals
• Maximal operators defined by Fourier multipliers

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